Let’s continue to work with algebra now to do “expansion” and “factorisation”.

Expansion

Expanding brackets involves removing the brackets from an expression by multiplying out the brackets. This is achieved by multiplying every term inside the bracket by the term outside the bracket.

Let's expand:

3(x+6)

• (3)(x + 6)
• (3)(x) + (3)(6) = 3x + 18

6(4a−10)

• (6)(4a + -10)
• (6)(4a) + (6)(-10) = 24a - 60

Factorisation

Factorisation is the opposite process of expanding brackets.

For example, expanding brackets would require 2(x+1) to be written as 2x+2. Factorisation would be to start with 2x+2 and to end up with 2(x+1).

Let's factorise:

2x+2

• What’s common in both? 2.
• 2(x + 1)

2x² + x - 3

• 2x² => 2x multiplied by x.
  
• To get “x” do -2x +3x
• To get -3 do 3 multiplied by -1 = -3
• (2x + 3)(x-1)

Example Question/s

Watch video for explanation of the following question/s:

Expand and simplify 7(x+2) + 5.

A 7x + 19 B 7x - 19 C 7x - 9 D -7x + 19 E None of these

Factorize and simplify a² – 6a + 9.

A (a – 3)(a – 3) B (a + 3)(a – 3) C (a + 3)(a + 3) D (a – 3)(a + 3) E None of these

Key rules to remember

• Expanding brackets involves removing the brackets from an expression by multiplying out the brackets. This is achieved by multiplying every term inside the bracket by the term outside the bracket.
• To factorise, take out common factors and then put the equation back together.

Practice time!

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